A shortstop is standing in the base path between second and third base when she fields the ball. She is 25 feet from second base and needs to make the throw to first base. Assuming the field is square, how far does she need to throw the ball? Round your answer to the nearest tenth.
(1 point)
feet
If the shortstop is standing in the base path between second and third base, and needs to make the throw to first base, she needs to throw the ball across the field diagonally. This forms a right triangle, with the distance from second base to first base as the hypotenuse and the distance from the shortstop to second base as one of the legs.
Using the Pythagorean theorem, we can calculate the distance she needs to throw the ball:
Distance^2 = (Distance from shortstop to second base)^2 + (Distance from second base to first base)^2
Distance^2 = 25^2 + 90^2
Distance^2 = 625 + 8100
Distance^2 = 8725
Distance ≈ 93.5 feet
Therefore, the shortstop needs to throw the ball approximately 93.5 feet.
To find the distance the shortstop needs to throw the ball, we can use the Pythagorean theorem. The base path from second base to third base forms a right triangle with the throw to first base.
The distance from second base to first base is the hypotenuse of the right triangle, and the distance from the shortstop to second base is one of the legs.
Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can find the distance needed to throw the ball.
Let's call the distance the shortstop needs to throw the ball "c."
The distance from second base to the shortstop is given as 25 feet, which we'll call "a."
The distance from the shortstop to first base, which we want to find, is "c."
Using the Pythagorean theorem, we can set up the equation:
c^2 = a^2 + b^2
Since we want to find "c," we can rearrange the equation to solve for it:
c^2 = 25^2 + b^2
Simplifying:
c^2 = 625 + b^2
To find the value of "b," we can use the fact that the field is square, and the distance from first to second base is the same as the distance from second to third base. Let's call this distance "x."
So, b = x.
Since the field is square, the distance from second to third base is also "x," and the distance from second base to first base is 2x.
To find "x," we need to solve the equation:
2x = 25
Dividing both sides by 2:
x = 12.5
Now we can substitute the value of "x" into the equation:
c^2 = 625 + (12.5)^2
Simplifying:
c^2 = 625 + 156.25
c^2 = 781.25
Taking the square root of both sides:
c = √781.25
c ≈ 27.9
Therefore, the shortstop needs to throw the ball approximately 27.9 feet. Rounded to the nearest tenth, the answer is 27.9 feet.
To find the distance she needs to throw the ball, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides.
In this case, we can consider the distance from the shortstop to second base as one side of the right triangle, the distance from second base to first base as the other side, and the distance she needs to throw the ball as the hypotenuse.
Let's calculate it step by step:
1. Calculate the square of the distance from the shortstop to second base:
25 feet x 25 feet = 625 square feet
2. Calculate the square of the distance from second base to first base:
This distance is unknown, so let's call it x.
Therefore, (x feet) x (x feet) = x² square feet.
3. Apply the Pythagorean theorem:
625 square feet + x² square feet = the square of the distance she needs to throw the ball.
4. Solve for x:
x² = the square of the distance she needs to throw the ball - 625 square feet
Since the field is square, the distance she needs to throw the ball is equal to the distance from home plate to second base, which is also 90 feet.
So, the equation becomes:
x² = 90 feet x 90 feet - 625 square feet
x² = 8100 square feet - 625 square feet
x² = 7475 square feet
5. Find the square root of both sides of the equation to get the distance she needs to throw the ball:
x = √7475
6. Finally, round the answer to the nearest tenth:
x ≈ 86.5 feet
Therefore, the shortstop needs to throw the ball approximately 86.5 feet to first base.